Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation

  • I. P. Mel'nichenko

Abstract

In commutative associative third-rank algebras with principal identity over a complex field, we select bases such that hypercomplex monogenic functions constructed in these bases have components satisfying the three-dimensional Laplace equation. The notion of monogeneity for these functions is similar to the notion of monogeneity in the complex plane.
Published
25.09.2003
How to Cite
Mel’nichenkoI. P. “Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 9, Sept. 2003, pp. 1284-90, https://umj.imath.kiev.ua/index.php/umj/article/view/4002.
Section
Short communications